Finite Impulse Response Filters - Digital Signal Processing in Power System Protection and Control - page 94

(a) (b)

1 0.4

h ()

H ()

0.2

0.5

0

0

0 5 10 15 20

kf = 50

50

-0.2

arg[ Hk ( )]

0 -0.4

-50 -0.6

0 5 10 15 20

0 5 10 15 20

n

kf = 50

(c) (d)

1.2 1.2

H ()

H () ω ω

1

1

0.8 0.8

0.6 0.6

0.4 0.4

0.2

0.2

0

0

0 200 400 600 800 1000

0 200 400 600 800 1000

ωπ 2

ω2

Fig. 6.17 Characteristics of the high-pass filter designed with frequency response sampling
method (Example 6.11): a assumed filter frequency response b filter impulse response c effective
filter frequency response d frequency response after application of Hamming window

Applying inverse Fourier transformation results in the following filter

coefficients:

h ð 0 Þ¼ h ð 19 Þ¼ 0 : 0503; h ð 1 Þ¼ h ð 18 Þ¼ 0 : 0077; h ð 2 Þ¼ h ð 17 Þ¼ 0;
h ð 3 Þ¼ h ð 16 Þ¼ 0 : 0848;
h ð 4 Þ¼ h ð 15 Þ¼ 0 : 018; h ð 5 Þ¼ h ð 14 Þ¼ 0 : 088; h ð 6 Þ¼ h ð 13 Þ¼ 0 : 1162;
h ð 7 Þ¼ h ð 12 Þ¼ 0;
h ð 8 Þ¼ h ð 11 Þ¼ 0 : 4061; h ð 9 Þ¼ h ð 10 Þ¼ 0 : 3914;

In Fig. 6.17 b-d the filter impulse response along with corresponding filter
spectrum and spectrum after application of Hamming window are presented. All
remarks from preceding examples apply also to this case (spectrum oscillations,
effects of smoothing window, effects of higher number of filter coefficients), thus
they will not be repeated here again.